Question

The population of a certain species of lizards decreases at a rate of 2 percent per year you counted 75 lizards in the habitat you are studying

a. is this exponential growth or decay?
b. what is the rate of growth or decay?
c. what was the initial amount?
d. what is the function?
e. how many years will it take for the population to drop below 50?

Answer 1

The population of lizards is decreasing at a rate of 2 percent per year. The initial population is 75. The population is undergoing exponential decay with a decay rate of 2 percent per year.

Step-by-step explanation:

a. The population shows exponential growth, as the number of lizards decreases at a fixed rate of 2 percent per year.

b. The rate of growth or decay is 2 percent per year, as stated in the problem.

c. The initial amount of lizards is 75, as given in the problem.

d. The function representing the population is: P(t) = P₀(1 - r)^t, where P(t) is the population at time t, P₀ is the initial population, r is the decay rate (0.02), and t is the time in years.

e. To find how many years it will take for the population to drop below 50, we can set up the following inequality: 75(1 - 0.02)^t < 50. Solving for t, we find that it will take approximately 15 years for the population to drop below 50.